Higher animals use some form of an "internal model" of themselves for planning complex actions and predicting their consequence, but it is not clear if and how these self-models are acquired or what form they take. Analogously, most practical robotic systems use internal mathematical models, but these are laboriously constructed by engineers. While simple yet robust behaviors can be achieved without a model at all, here we show how low-level sensation and actuation synergies can give rise to an internal predictive self-model, which in turn can be used to develop new behaviors.